Title

Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable

Authors

Ivan Correa, Universidad Metropolitana de Ciencias de la Educación
Irvin R. Hentzel, Iowa State UniversityFollow

Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2009

Journal or Book Title

Rocky Mountain Journal of Mathematics

Volume

39

Issue

3

First Page

757

Last Page

764

DOI

10.1216/RMJ-2009-39-3-757

Abstract

We study commutative, nonassociative algebras satisfying the identity

(1) ((yx)x)x = 0

We show that finitely generated algebras over a field K of characteristic ≠ 2 satisfying (1) are solvable. For x in an algebra A, define the multiplicatin operator R_x by yR_x = yx, for all y ∈ A. Our identify is then that R_x³ = 0.

Comments

This article is published as Correa, Ivan, and Irvin Roy Hentzel. "Commutative Finitely Generated Algebras Satisfying ((yx) x) x= 0 are Solvable." Rocky Mountain Journal of Mathematics 39, no. 3 (2009): 757-764. DOI: 10.1216/RMJ-2009-39-3-757. Posted with permission.

Copyright Owner

Rocky Mountain Mathematics Consortium

Copyright Date

2009

Language

en

File Format

application/pdf

Recommended Citation

Correa, Ivan and Hentzel, Irvin R., "Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable" (2009). Mathematics Publications. 131.
https://lib.dr.iastate.edu/math_pubs/131